The Physical Basis of The Direction of Time (The Frontiers ...

∑
j
¯F µν
j
:= ∑ j
2.4 The Absorber Theory of Radiation 37
1
[
]
F µν
ret,j
2
+ F µν
adv,j
−→ 0 , (2.38)
constitutes their cosmic absorber condition. Since the retarded or advanced
fields vanish by definition in the asymptotic past or future, respectively, so
must their time-reversed partner because of (2.38), and hence also their asymmetric
combination. Wheeler and Feynman then concluded by means of the
homogeneous Maxwell equations that the total asymmetric field would vanish
everywhere. This is just the required ‘boundary’ condition.
However, the consistency of this procedure is very questionable. A similar
problem would arise for an expanding and recollapsing Universe that
were sandwiched between two thermodynamically opposite radiation eras (absorbers
with opposite thermodynamical arrows of time) – see Sect. 5.3. As
explained in Sect. 2.1, the compatibility of double-ended (two-time) boundary
conditions is highly nontrivial – similar to an eigenvalue problem. This consistency
problem is particularly severe for a universe that remains optically
transparent and thus preserves information contained in the radiation such as
light (Davies and Twamley 1993).
In contrast to the physical absorbers of Sect. 2.2, the new absorber condition
is symmetric under time reversal. This fact led to many misunderstandings.
For example, rather than adding the vanishing antisymmetric term to
(2.36), one might as well subtract it in order to obtain the time-reversed representation
ma µ i = e ∑
i F µν
adv,j (zσ i )v i,ν − e [
]
i
F µν
ret,i
2
(zσ i ) − F µν
adv,i (zσ i ) v i,ν . (2.39)
j(≠i)
Although it is as correct as (2.37) under the absorber condition, (2.39) describes
advanced actions and a radiation reaction that leads to reverse damping
(exponential acceleration).
Therefore, Wheeler and Feynman’s absorber condition cannot explain the
observed radiation arrow. Neither (2.37) nor (2.39) would describe the local
empirical situation, which requires in general that only a limited number of
‘obvious sources’ contribute noticeably to the retarded sum (2.37). Otherwise,
retardation would never have been recognized. This means that the retarded
contribution of all ‘other’ sources (those which form the true universal absorber)
must interfere destructively (see Fig. 2.7):
∑
F µν
ret,i ≈ 0 ‘inside’ universal absorber . (2.40)
i ∈ absorbers
This is possible (except for the remaining thermal radiation) if the absorber
particles approach thermal equilibrium by means of collisions after having
been accelerated by retarded fields. Therefore, one cannot expect
∑
F µν
adv,i
≈ 0 ‘inside’ universal absorber (2.41)
i ∈ absorbers